A numerical investigation of the resonance of gas-filled microbubbles: resonance dependence on acoustic pressure amplitude

The general Keller–Herring equation for free gas bubbles is augmented by specific terms to describe the elasticity, viscosity and thickness of the encapsulating shell in ultrasound contrast agent microbubbles. A numerical investigation that analyses the acoustic backscatter from bubbles is employed to identify resonance frequencies that can be compared, for increasing driving pressure amplitude, with linear approximations obtained via analytical considerations. Calculations for bubbles of the size employed in diagnostic ultrasound, between 2 and 6 μm diameter, that are immersed in water and blood and exposed to monochromatic insonation, causing the bubbles to undergo stable cavitation, reveal that the resonance frequency diverges from the linear approximation as the pressure amplitude is increased. The shift in resonance, to lower frequency values, is found to be more pronounced for larger bubbles with the calculated value differing by up to 40% from the linear approximation. The results of this simulation might be potentially useful in preparation of formulations of ultrasound contrast agents with the specifically desired features, such as for instance resonance frequency.     

Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations

Summary. We examine the convergence characteristics of iterative methods based on a new preconditioning operator for solving the linear systems arising from discretization and linearization of the steady-state Navier-Stokes equations. With a combination of analytic and empirical results, we study the effects of fundamental parameters on convergence. We demonstrate that the preconditioned problem has an eigenvalue distribution consisting of a tightly clustered set together with a small number of outliers. The structure of these distributions is independent of the discretization mesh size, but the cardinality of the set of outliers increases slowly as the viscosity becomes smaller. These characteristics are directly correlated with the convergence properties of iterative solvers. Received August 5, 2000 / Published online June 20, 2001     

Multifractal PDF analysis for intermittent systems

The formula for probability density functions (PDFs) has been extended to include PDF for energy dissipation rates in addition to other PDFs such as for velocity fluctuations, velocity derivatives, fluid particle accelerations, energy transfer rates, etc., and it is shown that the formula actually explains various PDFs extracted from direct numerical simulations and experiments performed in a wind tunnel. It is also shown that the formula with appropriate zooming increment corresponding to experimental situation gives a new route to obtain the scaling exponents of velocity structure function, including intermittency exponent, out of PDFs of velocity fluctuations.     

An estimate of the heat fluxes to the surface of blunt bodies moving at hypersonic velocity in the atmosphere

The problem of the chemically equilibrium three-dimensional boundary layer on a blunt body which is in motion in the atmosphere is considered. A solution of the system of equations of the boundary layer is found by the method of successive approximations, and simple analytic expressions are written in the first approximation for the surface friction and heat flux coefficients. Formulae are obtained in the final form for estimating the convective heat flux in the neighbourhood of the critical point of spherical blunting.     

Hydrogen sorption properties of non-stoichiometric ZrMn2-based systems

Hydrogen sorption by several non-stoichiometric ZrMn₂-based alloys was studied at pressures up to 50 atm and over a temperature range from 23 to about 200°C. The dissociation pressure of the hydrides is raised by a factor of 500–1000 for ZrMn₂T_0.8 or ZrMn₂T_1.2 (T ≡; transition element or Cu) as the host material compared with that for ZrMn₂ as the host material. Among the hydrides studied, ZrMn₂Co_0.8-H exhibited the highest value for the plateau pressure. Measurements of the experimental densities of the non-stoichiometric host materials show good agreement with the substitutional model in which manganese and/or T partially replace zirconium at the zirconium sites. The hydrides have remarkably low heats of formation and entropies of 12–19 kJ (mol H₂)⁻¹ and 50–80 J (mol H₂)⁻¹ K⁻¹ respectively. The hydrogen absorption or desorption is extremely rapid, e.g. 90% of the hydrogen was released or absorbed in about 1 min. The hydrides studied exhibit features which strongly suggest that they have technological potential.     

The kinetics of reductions of some chloropentakis(alkylamine)cobalt(III), aquapentakis(alkylamine)cobalt(III), and trans(O,Cl)-chloroaminoacidatodiethylenetriaminecobalt(III) ions by aquavanadium(II), or aquachromium(II)

The rate of the reduction of chloropentakis(alkylamine)cobalt(III) ions, Co(Cl)(A)₅^staggered2+, (A₅ = (NH₃)₅, trans-(NH₂CH₃)(NH₃)₄, (NH₂CH₃)₅ and (n-NH₂C₃H₇)₅) by vanadium(II) decreases in the following order: (n-NH₂C₃H₇)₅ > (NH₂CH₃)₅ >trans-(NH₂CH₃)(NH₃)₄ > (NH₃)₅. The similar result on the effect of alkylamines on the rate of the reductions of aquapentakis(alkylamine)cobalt(III) ions, Co(H₂O)(A)₅^staggered3+ by vanadium(II) and chromium(II) was obtained. The rate constants of reductions of Co(Cl)(A)₅^staggered2+ by vanadium(II) could be correlated with the rate constants of the reaction of Co(Cl)(A)₅^staggered2+ with iron(II) by the equation of log k_V = 1.3 log k_Fe + 3.6, where k_V and k_Fe are the second-order rate constant of reductions by vanadium(II) and iron(II) respectively. The steric effect of the coordinated alkylamines on the rates of reductions of Co(Cl)(A)₅^staggered2+ and Co(H₂O)(A)₅^staggered3+ by vanadium(II) and the reduction of Co(H₂O)(A)₅^staggered2+ by chromium(II) is relatively small. The effects of concentrations of perchloric acid and N,N-dimethylformamide were examined for the reduction of trans-(O,Cl)Co(Cl)(gly)(dien)⁺ by vanadium(II), where gly and dien represent glycinate ion and diethylenetriamine respectively. An outer-sphere mechanism was suggested for the reductions of Co(Cl)(A)₅^staggered2+ and trans(O,Cl)Co(Cl)(gly)(dien)⁺ by vanadium(II) based on the experimental results obtained.     

Three‐unit semicircles curve: A compact 3D graphical representation of DNA sequences based on classifications of nucleotides

A new three‐dimensional graphical representation of DNA sequences, three‐unit semicircles (TUS)‐curve, which maps a given sequence into a dot sequences embedded in three‐unit semicircles, is proposed based on three biclassifications of nucleotides. TUS‐curve has the merit of compactness and could avoid the degeneracy and loss of information. The geometrical center of the curve, which indicates the distribution of base frequencies of the corresponding DNA sequence, is extracted and applied to analyze the similarity of various species. Phylogenetic tree of 11 species based on their first exons of β‐globin genes showed that the TUS‐curve is a powerful tool to get valuable biological information. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Strain-dependent internal parameters in hyperelastic biological materials

The behavior of hyperelastic energies depending on an internal parameter, which is a function of the deformation gradient, is discussed. As an example, the analysis of two models where the parameter describes the activation of a tetanized skeletal muscle tissue is presented. In those models, the activation parameter depends on the strain and it is shown the importance of considering the derivative of the parameter with respect to the strain in order to capture the proper stress–strain relations.